Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

Handling of missing data in long‐term clinical trials: a case study

Missing data in clinical trials is a well‐known problem, and the classical statistical methods used can be overly simple. This case study shows how well‐established missing data theory can be applied to efficacy data collected in a long‐term open‐label trial with a discontinuation rate of almost 50%. Satisfaction with treatment in chronically constipated patients was the efficacy measure assessed at baseline and every 3 months postbaseline. The improvement in treatment satisfaction from baseline was originally analyzed with a paired t‐test ignoring missing data and discarding the correlation structure of the longitudinal data. As the original analysis started from missing completely at random assumptions regarding the missing data process, the satisfaction data were re‐examined, and several missing at random (MAR) and missing not at random (MNAR) techniques resulted in adjusted estimate for the improvement in satisfaction over 12 months. Throughout the different sensitivity analyses, the effect sizes remained significant and clinically relevant. Thus, even for an open‐label trial design, sensitivity analysis, with different assumptions for the nature of dropouts (MAR or MNAR) and with different classes of models (selection, pattern‐mixture, or multiple imputation models), has been found useful and provides evidence towards the robustness of the original analyses; additional sensitivity analyses could be undertaken to further qualify robustness. Copyright © 2012 John Wiley & Sons, Ltd.     

Unconstrained parametrizations for variance-covariance matrices

The estimation of variance-covariance matrices through optimization of an objective function, such as a log-likelihood function, is usually a difficult numerical problem. Since the estimates should be positive semi-definite matrices, we must use constrained optimization, or employ a parametrization that enforces this condition. We describe here five different parametrizations for variance-covariance matrices that ensure positive definiteness, thus leaving the estimation problem unconstrained. We compare the parametrizations based on their computational efficiency and statistical interpretability. The results described here are particularly useful in maximum likelihood and restricted maximum likelihood estimation in linear and non-linear mixed-effects models, but are also applicable to other areas of statistics.     

Duration and Recurrence of Unemployment Benefits

Using administrative data for the period 2005–2010, we test for the existence of segmentation in the pool of the unemployed receiving benefits and investigate the factors associated with the duration and recurrence of the receipt of unemployment benefits in Spain. The results suggest the existence of (at least) three groups of individuals, each with different combinations of covered unemployment duration and recurrence. We also find that the impact of the employment crisis has been an increase in the average length of time spent receiving unemployment benefits and the recurrence. Our findings support the hypothesis that not only the heterogeneity but also the previous experience of receipt increase the expected duration of subsequent benefit periods.     

Bibliometric analysis of production planning and control (1990–2016)

Production Planning and Control (PPC) has been one of the primary publishing outlets for operations management research for nearly three decades. This paper presents bibliometric analysis of the journal from its inception through 2016. PPC was analysed from six different perspectives to provide reliable and in-depth information about the journal’s performance and development. The analysis considered the development of the journal itself, the countries of contributing authors, authors’ academic and practitioner organisation affiliations, the top publishing and most cited authors, the most cited articles, and finally the topics of published papers through analysis of titles, keywords and abstracts. It was found that the journal is considered an outlet for both practice and academic research, reflecting changes over time in the landscape of operations management.     

Mimetic contagion and speculative bubbles

Conclusion The present essay has focused on specularity as a type of intersubjectivitywithin self-referential systems. We have stressed the self-organizationaldimension of specular processes, which lead to the emergenceof collective objects around which the group structures itself. Rationalbubbles, sunspots, and conventions provided us with examples of thiskind of self-organization within self-referential groups. It seems thatwe have here a theoretical schema that can account for numeroussocial institutions. Such is the case with money, which the overlappinggenerations model shows to belong to the same problematic. We haveobserved that individual and collective representations play an essentialrole in the definition of specular dynamics. In fact, giving thecollectivity a means of interpreting and understanding the natural andsocial environment is a crucial function of these representations. Inspite of its great importance, this cognitive dimension of collectiverepresentations has hardly been explored in previous theorizing. Wehave given priority to a specific form of specularity, namely, mimetism,which is in our view at the very heart of financial processes. Far frombeing the aberration that traditional approaches deem it to be, imita-tion is one of the most important types of rationality in situations ofuncertain and in situations where the agents' outcomes are highlyinterdependent. Our central hypothesis amounts to considering thatthe emergence of speculative bubbles on various kinds of markets canbe explained in terms of mimetic dynamics. Should this hypothesis beconfirmed, it would be possible to account for a phenomenon that isoften observed, namely, the link between bubbles and a decrease inthe diversity of opinion on the market. In our approach, conventionsare taken to be the outcome of a mimetic process. Conventions are thesocial objects created by a unanimous mimetic polarization.     

Bivariate income distributions with lognormal conditionals

In this paper, the most general bivariate distribution with lognormal conditionals is fully characterized, using the methodology proposed by [3]. The properties of the new family are studied in detail, including marginal and conditional distributions, regression functions, dependence measures, moments and inequality measures. The new distribution is very broad, and contains as a particular case the classical bivariate lognormal distribution. Several subfamilies are studied and a generalization of the basic model is discussed. Finally, we present an empirical application. We estimate and compare the basic model proposed in the paper with a classical model, using data from the European Community Household Panel in different periods of time.     

Will They Ever Converge? Earnings of Immigrant and Canadian-born Workers over the Last Two Decades1

Using Census data covering the 1980–2000 period, this article examines what outcomes would be necessary for today's recent immigrant cohorts to achieve earnings parity with Canadian‐born workers. Our results show that today's recent immigrants would have to experience a drastic steepening of their relative age‐earnings profile in the near future for their earnings to converge with their Canadian‐born counterparts. The reason is simple: the greater relative earnings growth experienced by recent immigrant cohorts has only partially offset the drastic deterioration in their relative earnings at entry.     

Emotional displays in children's television programming

The facial expressions of emotion and the circumstances under which the expressions occurred in a sample of the most popular children's television programs were investigated in this study. Fifteen-second randomly selected intervals from episodes of five television programs were analyzed for displays of happiness, sadness, anger, fear, disgust, and surprise. In addition, the contexts in which the emotions occurred were examined. Results indicated that particular emotional expressions occurred at significantly different frequencies and that there was an association between emotional displays and emotion-contexts. The high rate of emotional displays found in television shows has implications for the development of knowledge regarding emotional display rules in viewers.We are grateful to Sharon Galligan for assistance in coding part of the data and to Carolyn Saarni and Amy Halberstadt for helpful comments on an earlier draft of this paper. This research was supported in part by a grant from the National Institute of Disabilities and Rehabilitation Research, #GOO85351. The opinions expressed herein do not necessarily reflect the position or policy of the U.S. Department of Education.